Question: Simplify the following expression: $(x^5+x^4+x+10)-(x^5+2x^4-x^3+12).$ Express your answer as a polynomial with the degrees of the terms in decreasing order.
Answer: We have \begin{align*}
&(x^5+x^4+x+10)-(x^5+2x^4-x^3+12)\\
&=(1-1)x^5+(1-2)x^4+(0-(-1))x^3+(1-0)x+(10-12)\\
&=\boxed{-x^4+x^3+x-2}
\end{align*}